The Legal Status of Heraldry in the US

There is a good deal of confusion among the general public about the
status of heraldry in the United States, due to the perceived link between
heraldry and nobility on the one hand, to the prohibition on titles of
nobility on the other hand.

No title of nobility shall be granted by the United States: and no
person holding any office of profit or trust under them, shall, without
the consent of the Congress, accept of any present, emolument, office,
or title, of any kind whatever, from any king, prince, or foreign state.

No state shall...grant any title of nobility.

The Constitution thus prohibits titles of nobility, but coat of arms
are not titles of nobility, nor are they necessarily the prerogative of
the nobility anyway. The US government is not in the habit of granting
or regulating coat of arms, although nothing prevents it from doing so.
But there aren't that many governments that are in such a habit to start
with. In fact, heraldry is somewhat alive in the US. States have seals,
Universities have coats, individuals used to and some still do. Here is
what a founding father had to say on the topic:

It is far from my design to intimate an opinion, that Heraldry, Coat-Armor,
etc. might not be rendered conducive to public and private use with us;
or that they can have any tendency unfriendly to the purest spirit of Republicanism.
On the contrary, a different conclusion is deducible from the practice
of Congress, and the states; all of which have established some kind of
Armorial Devices, to authenticate their official instruments.

George Washington

George (of a patrician bent, it is true) used his arms (Argent,
two bars beneath three mullets gules) on seals and book-plates. These
arms appear on the flag of the District of Columbia.